2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230972We study a trace formula for tamely ramified abelian varieties $A$ over a complete discretely valued field, which expresses the Euler characteristic of the special fiber of the Néron model of $A$ in terms of the Galois action on the $\ell$-adic cohomology of $A$. If $A$ has purely additive reduction, the trace formula yields a cohomological interpretation for the number of connected components of the special fiber of the Néron model.Main result (Conjecture 1.1) proven unconditionally; Conjecture 1.2 in version 1 was recently proven by Liu and Lorenzini (see [10])Algebraic Geometrytext